PHYS5523 Theory of Relativity
Test 2: The Gravitational Field of a Single Body
November 2, 2011
General Instructions: This is a three hour, open book test with three
problems. Complete all three problems.
Problem 1: A Radially Infalling Observer.
a) Demon
PHYS5523 Theory of Relativity
Test 1: Solutions
September 20, 2011
Problem 1: Circular Motion and Time Dilation.
In spherical polar coordinates the four acceleration and four velocity of this
obect must take on a particular simple form, given that we are
PHYS5523 Theory of Relativity
Test 1: Special Relativity
September 20, 2011
General Instructions: This is a two hour, open book test with three problems. Complete all three problems.
Problem 1: Circular Motion and Time Dilation.
Consider an object in a ci
Phys5523 Theory of Relativity
Lecturer: Daniel Kennefick
Office: Physics Room 237
Phone: (479) 575-6784
E-mail: danielk@uark.edu
Class website: http:/dafix.uark.edu/~danielk/Relativity/class.html
Classes: Mondays, Wednesdays and Fridays from 9:30 to 10:20
Three and a Half Principles: The Origins of
Modern Relativity Theory
Daniel Kenneck
June 9, 2011
1
Introduction
In 1900 the eld theory of electromagnetism, which owes it origins primarily
to the work of James Clerk Maxwell, had been under rapid developmen
PROBLEM 12.13 167
But since gm, 2 0 at 7' 2 2M and gm, 2 1, we conclude nr 2 0. A normal
vector is therefore,
71" 2 (1,0,0, 0) .
This is null because
11 ~ n 2 gm,(n)2 2 0
atr22M.
12-13.
a) An observer falls feet rst into a Schwarzschild black hole lo
PROBLEM 9.16 131
c) The rst integral (including the 2) is just the one in ( 9.54) and equals 27r.
Show that the second integral gives (7r/2)(u1 + U2) and that this equals
7r G'M/(f2 to lowest order in 1/c2.
d) Combine these results to derive (9.55).
So
66 CHAPTER 6. GRAVITATION AS GEOMETRY
b) The four-velocity in the (t, :13) frame can be calculated from the expression
for m(t) and y(t) given in Problem 6, together with the line element derived
in part (a) of that problem which gives the connecti
Q. 1
a) The simplest way to nd the radial velocity of an observer falling freely from innity is to note that
he begins his fall from rest at innity and thus l = 0 and dt/d = 1 which means e = 1. Since e and
l are constants of the motion we can simply plug